/***************************************************************************/
/*                                                                         */
/*  ftbbox.c                                                               */
/*                                                                         */
/*    FreeType bbox computation (body).                                    */
/*                                                                         */
/*  Copyright 1996-2001, 2002, 2004, 2006, 2010 by                         */
/*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
/*                                                                         */
/*  This file is part of the FreeType project, and may only be used        */
/*  modified and distributed under the terms of the FreeType project       */
/*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
/*  this file you indicate that you have read the license and              */
/*  understand and accept it fully.                                        */
/*                                                                         */
/***************************************************************************/


/*************************************************************************/
/*                                                                       */
/* This component has a _single_ role: to compute exact outline bounding */
/* boxes.                                                                */
/*                                                                       */
/*************************************************************************/


#include <ft2build.h>
#include FT_BBOX_H
#include FT_IMAGE_H
#include FT_OUTLINE_H
#include FT_INTERNAL_CALC_H
#include FT_INTERNAL_OBJECTS_H


typedef struct TBBox_Rec_
{
    FT_Vector last;
    FT_BBox bbox;

} TBBox_Rec;


/*************************************************************************/
/*                                                                       */
/* <Function>                                                            */
/*    BBox_Move_To                                                       */
/*                                                                       */
/* <Description>                                                         */
/*    This function is used as a `move_to' and `line_to' emitter during  */
/*    FT_Outline_Decompose().  It simply records the destination point   */
/*    in `user->last'; no further computations are necessary since we    */
/*    use the cbox as the starting bbox which must be refined.           */
/*                                                                       */
/* <Input>                                                               */
/*    to   :: A pointer to the destination vector.                       */
/*                                                                       */
/* <InOut>                                                               */
/*    user :: A pointer to the current walk context.                     */
/*                                                                       */
/* <Return>                                                              */
/*    Always 0.  Needed for the interface only.                          */
/*                                                                       */
static int
BBox_Move_To( FT_Vector *to,
              TBBox_Rec *user )
{
    user->last = *to;

    return 0;
}


#define CHECK_X( p, bbox )  \
          ( p->x < bbox.xMin || p->x > bbox.xMax )

#define CHECK_Y( p, bbox )  \
          ( p->y < bbox.yMin || p->y > bbox.yMax )


/*************************************************************************/
/*                                                                       */
/* <Function>                                                            */
/*    BBox_Conic_Check                                                   */
/*                                                                       */
/* <Description>                                                         */
/*    Finds the extrema of a 1-dimensional conic Bezier curve and update */
/*    a bounding range.  This version uses direct computation, as it     */
/*    doesn't need square roots.                                         */
/*                                                                       */
/* <Input>                                                               */
/*    y1  :: The start coordinate.                                       */
/*                                                                       */
/*    y2  :: The coordinate of the control point.                        */
/*                                                                       */
/*    y3  :: The end coordinate.                                         */
/*                                                                       */
/* <InOut>                                                               */
/*    min :: The address of the current minimum.                         */
/*                                                                       */
/*    max :: The address of the current maximum.                         */
/*                                                                       */
static void
BBox_Conic_Check( FT_Pos y1,
                  FT_Pos y2,
                  FT_Pos y3,
                  FT_Pos *min,
                  FT_Pos *max )
{
    if ( y1 <= y3 && y2 == y1 )
    {     /* flat arc */
        goto Suite;
    }

    if ( y1 < y3 )
    {
        if ( y2 >= y1 && y2 <= y3 )
        {   /* ascending arc */
            goto Suite;
        }
    }
    else
    {
        if ( y2 >= y3 && y2 <= y1 )   /* descending arc */
        {
            y2 = y1;
            y1 = y3;
            y3 = y2;
            goto Suite;
        }
    }

    y1 = y3 = y1 - FT_MulDiv( y2 - y1, y2 - y1, y1 - 2 * y2 + y3 );

    Suite:
    if ( y1 < *min )
    { *min = y1; }
    if ( y3 > *max )
    { *max = y3; }
}


/*************************************************************************/
/*                                                                       */
/* <Function>                                                            */
/*    BBox_Conic_To                                                      */
/*                                                                       */
/* <Description>                                                         */
/*    This function is used as a `conic_to' emitter during               */
/*    FT_Outline_Decompose().  It checks a conic Bezier curve with the   */
/*    current bounding box, and computes its extrema if necessary to     */
/*    update it.                                                         */
/*                                                                       */
/* <Input>                                                               */
/*    control :: A pointer to a control point.                           */
/*                                                                       */
/*    to      :: A pointer to the destination vector.                    */
/*                                                                       */
/* <InOut>                                                               */
/*    user    :: The address of the current walk context.                */
/*                                                                       */
/* <Return>                                                              */
/*    Always 0.  Needed for the interface only.                          */
/*                                                                       */
/* <Note>                                                                */
/*    In the case of a non-monotonous arc, we compute directly the       */
/*    extremum coordinates, as it is sufficiently fast.                  */
/*                                                                       */
static int
BBox_Conic_To( FT_Vector *control,
               FT_Vector *to,
               TBBox_Rec *user )
{
    /* we don't need to check `to' since it is always an `on' point, thus */
    /* within the bbox                                                    */

    if ( CHECK_X( control, user->bbox ))
    {
        BBox_Conic_Check( user->last.x,
                          control->x,
                          to->x,
                          &user->bbox.xMin,
                          &user->bbox.xMax );
    }

    if ( CHECK_Y( control, user->bbox ))
    {
        BBox_Conic_Check( user->last.y,
                          control->y,
                          to->y,
                          &user->bbox.yMin,
                          &user->bbox.yMax );
    }

    user->last = *to;

    return 0;
}


/*************************************************************************/
/*                                                                       */
/* <Function>                                                            */
/*    BBox_Cubic_Check                                                   */
/*                                                                       */
/* <Description>                                                         */
/*    Finds the extrema of a 1-dimensional cubic Bezier curve and        */
/*    updates a bounding range.  This version uses splitting because we  */
/*    don't want to use square roots and extra accuracy.                 */
/*                                                                       */
/* <Input>                                                               */
/*    p1  :: The start coordinate.                                       */
/*                                                                       */
/*    p2  :: The coordinate of the first control point.                  */
/*                                                                       */
/*    p3  :: The coordinate of the second control point.                 */
/*                                                                       */
/*    p4  :: The end coordinate.                                         */
/*                                                                       */
/* <InOut>                                                               */
/*    min :: The address of the current minimum.                         */
/*                                                                       */
/*    max :: The address of the current maximum.                         */
/*                                                                       */

#if 0

static void
BBox_Cubic_Check( FT_Pos   p1,
                  FT_Pos   p2,
                  FT_Pos   p3,
                  FT_Pos   p4,
                  FT_Pos*  min,
                  FT_Pos*  max )
{
  FT_Pos  stack[32*3 + 1], *arc;


  arc = stack;

  arc[0] = p1;
  arc[1] = p2;
  arc[2] = p3;
  arc[3] = p4;

  do
  {
    FT_Pos  y1 = arc[0];
    FT_Pos  y2 = arc[1];
    FT_Pos  y3 = arc[2];
    FT_Pos  y4 = arc[3];


    if ( y1 == y4 )
    {
      if ( y1 == y2 && y1 == y3 )                         /* flat */
        goto Test;
    }
    else if ( y1 < y4 )
    {
      if ( y2 >= y1 && y2 <= y4 && y3 >= y1 && y3 <= y4 ) /* ascending */
        goto Test;
    }
    else
    {
      if ( y2 >= y4 && y2 <= y1 && y3 >= y4 && y3 <= y1 ) /* descending */
      {
        y2 = y1;
        y1 = y4;
        y4 = y2;
        goto Test;
      }
    }

    /* unknown direction -- split the arc in two */
    arc[6] = y4;
    arc[1] = y1 = ( y1 + y2 ) / 2;
    arc[5] = y4 = ( y4 + y3 ) / 2;
    y2 = ( y2 + y3 ) / 2;
    arc[2] = y1 = ( y1 + y2 ) / 2;
    arc[4] = y4 = ( y4 + y2 ) / 2;
    arc[3] = ( y1 + y4 ) / 2;

    arc += 3;
    goto Suite;

 Test:
    if ( y1 < *min ) *min = y1;
    if ( y4 > *max ) *max = y4;
    arc -= 3;

  Suite:
    ;
  } while ( arc >= stack );
}

#else

static void
test_cubic_extrema( FT_Pos y1,
                    FT_Pos y2,
                    FT_Pos y3,
                    FT_Pos y4,
                    FT_Fixed u,
                    FT_Pos *min,
                    FT_Pos *max )
{
    /* FT_Pos    a = y4 - 3*y3 + 3*y2 - y1; */
    FT_Pos b = y3 - 2 * y2 + y1;
    FT_Pos c = y2 - y1;
    FT_Pos d = y1;
    FT_Pos y;
    FT_Fixed uu;

    FT_UNUSED ( y4 );


    /* The polynomial is                      */
    /*                                        */
    /*    P(x) = a*x^3 + 3b*x^2 + 3c*x + d  , */
    /*                                        */
    /*   dP/dx = 3a*x^2 + 6b*x + 3c         . */
    /*                                        */
    /* However, we also have                  */
    /*                                        */
    /*   dP/dx(u) = 0                       , */
    /*                                        */
    /* which implies by subtraction that      */
    /*                                        */
    /*   P(u) = b*u^2 + 2c*u + d            . */

    if ( u > 0 && u < 0x10000L )
    {
        uu = FT_MulFix( u, u );
        y = d + FT_MulFix( c, 2 * u ) + FT_MulFix( b, uu );

        if ( y < *min )
        { *min = y; }
        if ( y > *max )
        { *max = y; }
    }
}


static void
BBox_Cubic_Check( FT_Pos y1,
                  FT_Pos y2,
                  FT_Pos y3,
                  FT_Pos y4,
                  FT_Pos *min,
                  FT_Pos *max )
{
    /* always compare first and last points */
    if ( y1 < *min )
    { *min = y1; }
    else if ( y1 > *max )
    { *max = y1; }

    if ( y4 < *min )
    { *min = y4; }
    else if ( y4 > *max )
    { *max = y4; }

    /* now, try to see if there are split points here */
    if ( y1 <= y4 )
    {
        /* flat or ascending arc test */
        if ( y1 <= y2 && y2 <= y4 && y1 <= y3 && y3 <= y4 )
        {
            return;
        }
    }
    else /* y1 > y4 */
    {
        /* descending arc test */
        if ( y1 >= y2 && y2 >= y4 && y1 >= y3 && y3 >= y4 )
        {
            return;
        }
    }

    /* There are some split points.  Find them. */
    {
        FT_Pos a = y4 - 3 * y3 + 3 * y2 - y1;
        FT_Pos b = y3 - 2 * y2 + y1;
        FT_Pos c = y2 - y1;
        FT_Pos d;
        FT_Fixed t;


        /* We need to solve `ax^2+2bx+c' here, without floating points!      */
        /* The trick is to normalize to a different representation in order  */
        /* to use our 16.16 fixed point routines.                            */
        /*                                                                   */
        /* We compute FT_MulFix(b,b) and FT_MulFix(a,c) after normalization. */
        /* These values must fit into a single 16.16 value.                  */
        /*                                                                   */
        /* We normalize a, b, and c to `8.16' fixed float values to ensure   */
        /* that its product is held in a `16.16' value.                      */

        {
            FT_ULong t1, t2;
            int shift = 0;


            /* The following computation is based on the fact that for   */
            /* any value `y', if `n' is the position of the most         */
            /* significant bit of `abs(y)' (starting from 0 for the      */
            /* least significant bit), then `y' is in the range          */
            /*                                                           */
            /*   -2^n..2^n-1                                             */
            /*                                                           */
            /* We want to shift `a', `b', and `c' concurrently in order  */
            /* to ensure that they all fit in 8.16 values, which maps    */
            /* to the integer range `-2^23..2^23-1'.                     */
            /*                                                           */
            /* Necessarily, we need to shift `a', `b', and `c' so that   */
            /* the most significant bit of its absolute values is at     */
            /* _most_ at position 23.                                    */
            /*                                                           */
            /* We begin by computing `t1' as the bitwise `OR' of the     */
            /* absolute values of `a', `b', `c'.                         */

            t1 = ( FT_ULong ) (( a >= 0 ) ? a : -a );
            t2 = ( FT_ULong ) (( b >= 0 ) ? b : -b );
            t1 |= t2;
            t2 = ( FT_ULong ) (( c >= 0 ) ? c : -c );
            t1 |= t2;

            /* Now we can be sure that the most significant bit of `t1'  */
            /* is the most significant bit of either `a', `b', or `c',   */
            /* depending on the greatest integer range of the particular */
            /* variable.                                                 */
            /*                                                           */
            /* Next, we compute the `shift', by shifting `t1' as many    */
            /* times as necessary to move its MSB to position 23.  This  */
            /* corresponds to a value of `t1' that is in the range       */
            /* 0x40_0000..0x7F_FFFF.                                     */
            /*                                                           */
            /* Finally, we shift `a', `b', and `c' by the same amount.   */
            /* This ensures that all values are now in the range         */
            /* -2^23..2^23, i.e., they are now expressed as 8.16         */
            /* fixed-float numbers.  This also means that we are using   */
            /* 24 bits of precision to compute the zeros, independently  */
            /* of the range of the original polynomial coefficients.     */
            /*                                                           */
            /* This algorithm should ensure reasonably accurate values   */
            /* for the zeros.  Note that they are only expressed with    */
            /* 16 bits when computing the extrema (the zeros need to     */
            /* be in 0..1 exclusive to be considered part of the arc).   */

            if ( t1 == 0 )
            {  /* all coefficients are 0! */
                return;
            }

            if ( t1 > 0x7FFFFFUL )
            {
                do
                {
                    shift++;
                    t1 >>= 1;

                }
                while ( t1 > 0x7FFFFFUL );

                /* this loses some bits of precision, but we use 24 of them */
                /* for the computation anyway                               */
                a >>= shift;
                b >>= shift;
                c >>= shift;
            }
            else if ( t1 < 0x400000UL )
            {
                do
                {
                    shift++;
                    t1 <<= 1;

                }
                while ( t1 < 0x400000UL );

                a <<= shift;
                b <<= shift;
                c <<= shift;
            }
        }

        /* handle a == 0 */
        if ( a == 0 )
        {
            if ( b != 0 )
            {
                t = -FT_DivFix( c, b ) / 2;
                test_cubic_extrema( y1, y2, y3, y4, t, min, max );
            }
        }
        else
        {
            /* solve the equation now */
            d = FT_MulFix( b, b ) - FT_MulFix( a, c );
            if ( d < 0 )
            {
                return;
            }

            if ( d == 0 )
            {
                /* there is a single split point at -b/a */
                t = -FT_DivFix( b, a );
                test_cubic_extrema( y1, y2, y3, y4, t, min, max );
            }
            else
            {
                /* there are two solutions; we need to filter them */
                d = FT_SqrtFixed(( FT_Int32 ) d );
                t = -FT_DivFix( b - d, a );
                test_cubic_extrema( y1, y2, y3, y4, t, min, max );

                t = -FT_DivFix( b + d, a );
                test_cubic_extrema( y1, y2, y3, y4, t, min, max );
            }
        }
    }
}

#endif


/*************************************************************************/
/*                                                                       */
/* <Function>                                                            */
/*    BBox_Cubic_To                                                      */
/*                                                                       */
/* <Description>                                                         */
/*    This function is used as a `cubic_to' emitter during               */
/*    FT_Outline_Decompose().  It checks a cubic Bezier curve with the   */
/*    current bounding box, and computes its extrema if necessary to     */
/*    update it.                                                         */
/*                                                                       */
/* <Input>                                                               */
/*    control1 :: A pointer to the first control point.                  */
/*                                                                       */
/*    control2 :: A pointer to the second control point.                 */
/*                                                                       */
/*    to       :: A pointer to the destination vector.                   */
/*                                                                       */
/* <InOut>                                                               */
/*    user     :: The address of the current walk context.               */
/*                                                                       */
/* <Return>                                                              */
/*    Always 0.  Needed for the interface only.                          */
/*                                                                       */
/* <Note>                                                                */
/*    In the case of a non-monotonous arc, we don't compute directly     */
/*    extremum coordinates, we subdivide instead.                        */
/*                                                                       */
static int
BBox_Cubic_To( FT_Vector *control1,
               FT_Vector *control2,
               FT_Vector *to,
               TBBox_Rec *user )
{
    /* we don't need to check `to' since it is always an `on' point, thus */
    /* within the bbox                                                    */

    if ( CHECK_X( control1, user->bbox ) ||
         CHECK_X( control2, user->bbox ))
    {
        BBox_Cubic_Check( user->last.x,
                          control1->x,
                          control2->x,
                          to->x,
                          &user->bbox.xMin,
                          &user->bbox.xMax );
    }

    if ( CHECK_Y( control1, user->bbox ) ||
         CHECK_Y( control2, user->bbox ))
    {
        BBox_Cubic_Check( user->last.y,
                          control1->y,
                          control2->y,
                          to->y,
                          &user->bbox.yMin,
                          &user->bbox.yMax );
    }

    user->last = *to;

    return 0;
}

FT_DEFINE_OUTLINE_FUNCS( bbox_interface,
                         ( FT_Outline_MoveTo_Func ) BBox_Move_To,
                         ( FT_Outline_LineTo_Func ) BBox_Move_To,
                         ( FT_Outline_ConicTo_Func ) BBox_Conic_To,
                         ( FT_Outline_CubicTo_Func ) BBox_Cubic_To,
                         0, 0
)

/* documentation is in ftbbox.h */

FT_EXPORT_DEF( FT_Error )
FT_Outline_Get_BBox( FT_Outline *outline,
                     FT_BBox *abbox )
{
    FT_BBox cbox;
    FT_BBox bbox;
    FT_Vector *vec;
    FT_UShort n;


    if ( !abbox )
    {
        return FT_Err_Invalid_Argument;
    }

    if ( !outline )
    {
        return FT_Err_Invalid_Outline;
    }

    /* if outline is empty, return (0,0,0,0) */
    if ( outline->n_points == 0 || outline->n_contours <= 0 )
    {
        abbox->xMin = abbox->xMax = 0;
        abbox->yMin = abbox->yMax = 0;
        return 0;
    }

    /* We compute the control box as well as the bounding box of  */
    /* all `on' points in the outline.  Then, if the two boxes    */
    /* coincide, we exit immediately.                             */

    vec = outline->points;
    bbox.xMin = bbox.xMax = cbox.xMin = cbox.xMax = vec->x;
    bbox.yMin = bbox.yMax = cbox.yMin = cbox.yMax = vec->y;
    vec++;

    for ( n = 1; n < outline->n_points; n++ )
    {
        FT_Pos x = vec->x;
        FT_Pos y = vec->y;


        /* update control box */
        if ( x < cbox.xMin )
        { cbox.xMin = x; }
        if ( x > cbox.xMax )
        { cbox.xMax = x; }

        if ( y < cbox.yMin )
        { cbox.yMin = y; }
        if ( y > cbox.yMax )
        { cbox.yMax = y; }

        if ( FT_CURVE_TAG( outline->tags[ n ] ) == FT_CURVE_TAG_ON )
        {
            /* update bbox for `on' points only */
            if ( x < bbox.xMin )
            { bbox.xMin = x; }
            if ( x > bbox.xMax )
            { bbox.xMax = x; }

            if ( y < bbox.yMin )
            { bbox.yMin = y; }
            if ( y > bbox.yMax )
            { bbox.yMax = y; }
        }

        vec++;
    }

    /* test two boxes for equality */
    if ( cbox.xMin < bbox.xMin || cbox.xMax > bbox.xMax ||
         cbox.yMin < bbox.yMin || cbox.yMax > bbox.yMax )
    {
        /* the two boxes are different, now walk over the outline to */
        /* get the Bezier arc extrema.                               */

        FT_Error error;
        TBBox_Rec user;

#ifdef FT_CONFIG_OPTION_PIC
        FT_Outline_Funcs bbox_interface;
        Init_Class_bbox_interface(&bbox_interface);
#endif

        user.bbox = bbox;

        error = FT_Outline_Decompose( outline, &bbox_interface, &user );
        if ( error )
        {
            return error;
        }

        *abbox = user.bbox;
    }
    else
    {
        *abbox = bbox;
    }

    return FT_Err_Ok;
}


/* END */
